Turning up the edges of the sheet metal will result in the 20 inches of
metal being divided into x inches of the first side, then the unknown
width of the gutter (let's call it "y") and then again x inches for the
second side.
As a picture:
x|______|x/y
As a formula:
20 = x + y + x = 2x + y
Resolving this to y we get:
20 - 2x = y
and switching it around:
y = 20 - 2x,
Now for part b) of your question:
The area of the gutter's cross-section is its width (y) multiplied with its height (x).
A(x,y) = x * y
If we use our result from a) to eliminate y then we can see that
A(x) = x * y = x * (20-2x) = 20x-2x^2
So I'd say that the answer to part b) should be:
A(x) = 20x - 2x^2
